/* --------------------------------------------------------------------------
CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-17 Bradley M. Bell

CppAD is distributed under multiple licenses. This distribution is under
the terms of the
                    Eclipse Public License Version 1.0.

A copy of this license is included in the COPYING file of this distribution.
Please visit http://www.coin-or.org/CppAD/ for information on other licenses.
-------------------------------------------------------------------------- */

/*
$begin rev_sparse_jac.cpp$$
$spell
	Jacobian
	Jac
	Dep
	Cpp
$$

$section Reverse Mode Jacobian Sparsity: Example and Test$$
$mindex RevSparseJac sparsity$$


$code
$srcfile%example/sparse/rev_sparse_jac.cpp%0%// BEGIN C++%// END C++%1%$$
$$

$end
*/
// BEGIN C++

# include <cppad/cppad.hpp>
namespace { // -------------------------------------------------------------
// define the template function BoolCases<Vector>
template <typename Vector>  // vector class, elements of type bool
bool BoolCases(void)
{	bool ok = true;
	using CppAD::AD;

	// domain space vector
	size_t n = 2;
	CPPAD_TESTVECTOR(AD<double>) ax(n);
	ax[0] = 0.;
	ax[1] = 1.;

	// declare independent variables and start recording
	CppAD::Independent(ax);

	// range space vector
	size_t m = 3;
	CPPAD_TESTVECTOR(AD<double>) ay(m);
	ay[0] = ax[0];
	ay[1] = ax[0] * ax[1];
	ay[2] = ax[1];

	// create f: x -> y and stop tape recording
	CppAD::ADFun<double> f(ax, ay);

	// sparsity pattern for the identity matrix
	Vector r(m * m);
	size_t i, j;
	for(i = 0; i < m; i++)
	{	for(j = 0; j < m; j++)
			r[ i * m + j ] = (i == j);
	}

	// sparsity pattern for F'(x)
	Vector s(m * n);
	s = f.RevSparseJac(m, r);

	// check values
	ok &= (s[ 0 * n + 0 ] == true);  // y[0] does     depend on x[0]
	ok &= (s[ 0 * n + 1 ] == false); // y[0] does not depend on x[1]
	ok &= (s[ 1 * n + 0 ] == true);  // y[1] does     depend on x[0]
	ok &= (s[ 1 * n + 1 ] == true);  // y[1] does     depend on x[1]
	ok &= (s[ 2 * n + 0 ] == false); // y[2] does not depend on x[0]
	ok &= (s[ 2 * n + 1 ] == true);  // y[2] does     depend on x[1]

	// sparsity pattern for F'(x)^T, note R is the identity, so R^T = R
	bool transpose = true;
	Vector st(n * m);
	st = f.RevSparseJac(m, r, transpose);

	// check values
	ok &= (st[ 0 * m + 0 ] == true);  // y[0] does     depend on x[0]
	ok &= (st[ 1 * m + 0 ] == false); // y[0] does not depend on x[1]
	ok &= (st[ 0 * m + 1 ] == true);  // y[1] does     depend on x[0]
	ok &= (st[ 1 * m + 1 ] == true);  // y[1] does     depend on x[1]
	ok &= (st[ 0 * m + 2 ] == false); // y[2] does not depend on x[0]
	ok &= (st[ 1 * m + 2 ] == true);  // y[2] does     depend on x[1]

	return ok;
}
// define the template function SetCases<Vector>
template <typename Vector>  // vector class, elements of type std::set<size_t>
bool SetCases(void)
{	bool ok = true;
	using CppAD::AD;

	// domain space vector
	size_t n = 2;
	CPPAD_TESTVECTOR(AD<double>) ax(n);
	ax[0] = 0.;
	ax[1] = 1.;

	// declare independent variables and start recording
	CppAD::Independent(ax);

	// range space vector
	size_t m = 3;
	CPPAD_TESTVECTOR(AD<double>) ay(m);
	ay[0] = ax[0];
	ay[1] = ax[0] * ax[1];
	ay[2] = ax[1];

	// create f: x -> y and stop tape recording
	CppAD::ADFun<double> f(ax, ay);

	// sparsity pattern for the identity matrix
	Vector r(m);
	size_t i;
	for(i = 0; i < m; i++)
	{	assert( r[i].empty() );
		r[i].insert(i);
	}

	// sparsity pattern for F'(x)
	Vector s(m);
	s = f.RevSparseJac(m, r);

	// check values
	bool found;

	// y[0] does     depend on x[0]
	found = s[0].find(0) != s[0].end();  ok &= (found == true);
	// y[0] does not depend on x[1]
	found = s[0].find(1) != s[0].end();  ok &= (found == false);
	// y[1] does     depend on x[0]
	found = s[1].find(0) != s[1].end();  ok &= (found == true);
	// y[1] does     depend on x[1]
	found = s[1].find(1) != s[1].end();  ok &= (found == true);
	// y[2] does not depend on x[0]
	found = s[2].find(0) != s[2].end();  ok &= (found == false);
	// y[2] does     depend on x[1]
	found = s[2].find(1) != s[2].end();  ok &= (found == true);

	// sparsity pattern for F'(x)^T
	bool transpose = true;
	Vector st(n);
	st = f.RevSparseJac(m, r, transpose);

	// y[0] does     depend on x[0]
	found = st[0].find(0) != st[0].end();  ok &= (found == true);
	// y[0] does not depend on x[1]
	found = st[1].find(0) != st[1].end();  ok &= (found == false);
	// y[1] does     depend on x[0]
	found = st[0].find(1) != st[0].end();  ok &= (found == true);
	// y[1] does     depend on x[1]
	found = st[1].find(1) != st[1].end();  ok &= (found == true);
	// y[2] does not depend on x[0]
	found = st[0].find(2) != st[0].end();  ok &= (found == false);
	// y[2] does     depend on x[1]
	found = st[1].find(2) != st[1].end();  ok &= (found == true);

	return ok;
}
} // End empty namespace
# include <vector>
# include <valarray>
bool RevSparseJac(void)
{	bool ok = true;
	// Run with Vector equal to four different cases
	// all of which are Simple Vectors with elements of type bool.
	ok &= BoolCases< CppAD::vectorBool     >();
	ok &= BoolCases< CppAD::vector  <bool> >();
	ok &= BoolCases< std::vector    <bool> >();
	ok &= BoolCases< std::valarray  <bool> >();


	// Run with Vector equal to two different cases both of which are
	// Simple Vectors with elements of type std::set<size_t>
	typedef std::set<size_t> set;
	ok &= SetCases< CppAD::vector  <set> >();
	ok &= SetCases< std::vector    <set> >();

	// Do not use valarray because its element access in the const case
	// returns a copy instead of a reference
	// ok &= SetCases< std::valarray  <set> >();

	return ok;
}

// END C++
